**Lecture 8** Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place.

**Lecture 8 – Tuesday 2/5/2013** • Block 1: Mole Balances • Block 2: Rate Laws • Block 3: Stoichiometry • Block 4: Combine • Pressure Drop • Liquid Phase Reactions • Gas Phase Reactions • Engineering Analysis of Pressure Drop

**Pressure Drop in PBRs** Concentration Flow System: Gas Phase Flow System:

**Pressure Drop in PBRs** Note: Pressure Drop does NOT affect liquid phase reactions Sample Question: Analyze the following second order gas phase reaction that occurs isothermally in a PBR: AB Mole Balances Must use the differential form of the mole balance to separate variables: Rate Laws Second order in A and irreversible:

**Pressure Drop in PBRs** Stoichiometry Isothermal, T=T0 Combine: Need to find (P/P0) as a function of W (or V if you have a PFR)

**Pressure Drop in PBRs** ErgunEquation: Constant mass flow:

**Pressure Drop in PBRs** Variable Density Let

**Pressure Drop in PBRs** Where CatalystWeight Let

**Pressure Drop in PBRs** Wewilluse this form for singlereactions: Isothermal case

**Pressure Drop in PBRs** and or The two expressions are coupledordinary differential equations. Wecanonlysolvethemsimultaneouslyusing an ODE solversuch as Polymath. For the special case of isothermal operation and epsilon = 0, we can obtain an analytical solution. Polymath will combine the Mole Balances, Rate Laws and Stoichiometry.

**Packed Bed Reactors**

**Pressure Drop in a PBR** 1 P W

**Concentration Profile in a PBR** 2 CA W

**Reaction Rate in a PBR** 3 -rA W

**Conversion in a PBR** 4 X W

**Flow Rate in a PBR** 5 1 W

**Example 1:Gas Phase Reaction in PBR for δ=0** Gas Phase reaction in PBR with δ = 0 (Analytical Solution) A + B 2C Repeat the previous one with equimolar feed of A and B and: kA = 1.5dm6/mol/kg/min α = 0.0099 kg-1 Find X at 100 kg

**Example 1:Gas Phase Reaction in PBR for δ=0** 1) Mole Balance 2) Rate Law 3) Stoichiometry

**Example 1:Gas Phase Reaction in PBR for δ=0** , , 4) Combine

**Example 1:Gas Phase Reaction in PBR for δ=0**

**Example 2:Gas Phase Reaction in PBR for δ≠0** The reaction A + 2B C is carried out in a packed bed reactor in which there is pressure drop. The feed is stoichiometric in A and B. Plot the conversion and pressure ratio y = P/P0 as a function of catalyst weight up to 100 kg. Additional Information kA = 6 dm9/mol2/kg/min α = 0.02 kg-1

**Example 2:Gas Phase Reaction in PBR for δ≠0** A + 2B C 3) Stoichiometry: Gas, Isothermal 1) Mole Balance 2) Rate Law

**Example 2:Gas Phase Reaction in PBR for δ≠0** 4) 7) 6) 5) Initial values: W=0, X=0, y=1 Final values: W=100 Combine with Polymath. If δ≠0, polymath must be used to solve.

**Example 2:Gas Phase Reaction in PBR for δ≠0**

**Example 2:Gas Phase Reaction in PBR for δ≠0**

**T = T0**

**Robert the Worrier wonders: What if we increase the** catalyst size by a factor of 2?

**Pressure DropEngineering Analysis**

**Pressure DropEngineering Analysis**

**Pressure DropEngineering Analysis**

**Heat Effects** Isothermal Design Stoichiometry Rate Laws Mole Balance

**End of Lecture 8**

**Pressure Drop - Summary** • Pressure Drop • Liquid Phase Reactions • Pressure Drop does not affect concentrations in lquid phase reactions. • Gas Phase Reactions • Epsilon does not equal to zero d(P)/d(W)=… Polymath will combine with d(X)/d(W) =… for you • Epsilon = 0 and isothermal P=f(W) Combine then separate variables (X,W) and integrate • Engineering Analysis of Pressure Drop

**Pressure Change – Molar Flow Rate** Use for heat effects, multiple rxns Isothermal: T = T0

**Example 1:Gas Phase Reaction in PBR for δ=0** A + B 2C Case 1: Case 2:

**PBR**